Question

What is the S.I. unit of wave number?
(A) $s$
(B) ${s^{ - 1}}$
(C) $m$
(D)${m^{ - 1}}$

Answer 1

The relationship of wavenumber and wavelength, can determine the S.I. unit of wave number easily. Wave number is the spatial frequency of a wave, measured in cycle per unit distance or radian per unit distance. Whereas temporal frequency can be thought as the number of waves per unit time, wave number is the number of waves per unit distance. Wavelength is the distance between identical points in the adjacent cycles of a waveform signal propagated in space or along a wire. This length is usually specified in metres $(m)$, centimetres $(cm)$, or millimetres $(mm)$.

Complete step by step answer:
Wave number is also known as propagation number or angular wave number is defined as the number of wavelength per unit distance the spatial wave frequency and is known as spatial frequency. It is a scalar quantity
Since the unit of wavelength is a metre. Because of this reason the unit of wave number is the inverse of a metre. And the mathematical representation is given as follows:
$k = \dfrac{1}{\lambda }$
$k$is the wave number.
$\lambda$ is the wavelength.

Therefore, the correct option is (D) ${m^{ - 1}}$ .

Note: Wave number can be used to specific quantities. A complex-valued wave number can be defined for a medium with complex-valued relative permittivity, relative permeability and reflective index.
In theoretical physics: it is the number of radians present in the unit distance.
Wavenumber equation: In general, we assume wave number is a characteristic of a wave and is constant for a wave. It varies from one wave to another wave. But there are some special cases where the value can be dynamic.
In spectroscopy: The angular wavenumber $k$ is given by.
k = \dfrac{{2\pi }}{\lambda }$$$$ = \dfrac{{2\pi \vartheta }}{{{\vartheta _p}}}$$$$ = \dfrac{\omega }{{{\vartheta _p}}}
Where,${\vartheta _p}$ is the phase velocity of a wave, $\omega = 2\pi \vartheta$ is the angular frequency.